City dominated the first half and deservedly led through Yaya Toure's sixth goal of the season just before the interval.
Lambert, whose side survived a relegation scare last season, was unwilling to say whether it was his best result since taking charge at Villa last year.
He said: "There have been (other) big games and big results, big moments at certain times.
"But this is a fabulous achievement because of the magnitude of their club and the players they have got.
"Where I will say it was very pleasing is that we had to come back twice.
"We have made a really good start in the league.
"It has been one hell of a start but we have come through it and are playing with a lot of confidence."
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